A characterization of $\omega$-limit sets in subshifts of Baire space

TL;DR

This paper investigates the structure of omega-limit sets in subshifts of Baire space, revealing limitations of classical theorems and providing new characterizations for specific types.

Contribution

It introduces new characterizations of omega-limit sets in subshifts of finite and bounded types, highlighting where classical results do not apply.

Findings

Classical structure theorems often fail in Baire space subshifts.

Characterizations of omega-limit sets are obtained for subshifts of finite types.

Attracting omega-limit sets are characterized in subshifts of bounded type.

Abstract

In this paper we consider the structure of $\omega$-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for $\omega$-limit sets fail in this context. Nevertheless, we obtain characterizations of $\omega$-limit sets in subshift of finite types and of attracting $\omega$-limit sets in subshifts of bounded type.